Complete MDP convolutional codes
Complete MDP convolutional codes
复制标题
完整的MDP卷积码
DOI：
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发表时间：
2017
影响因子：
0.8
通讯作者：
Julia Lieb
中科院分区：
文献类型：
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作者：
Julia Lieb
最大距离分布(MDP)卷积码具有其列距离尽可能大的特性。已经证明，在擦除信道上传输时，对于特定长度的窗口，这些码具有最佳的恢复率。反向MDP卷积码还有一个额外的优点，即它们适用于前向和后向译码算法。除此之外，完全MDP卷积码的子类能够减少译码期间的等待时间。本文的第一个主要结果是证明了具有[公式：见文本]的所有码参数的完全MDP卷积码的存在性和通用性，以及如果[公式：见文本]，则完全MDP卷积码不存在。第二个主要贡献是介绍了获得完整MDP卷积码的两种具体构造技术。这些构造适用于使用[公式：参见文本]的所有代码参数，但要求基础基字段的大小(足够)大。
Maximum distance profile (MDP) convolutional codes have the property that their column distances are as large as possible. It has been shown that, transmitting over an erasure channel, these codes have optimal recovery rate for windows of a certain length. Reverse MDP convolutional codes have the additional advantage that they are suitable for forward and backward decoding algorithms. Beyond that the subclass of complete MDP convolutional codes has the ability to reduce the waiting time during decoding. The first main result of this paper is to show the existence and genericity of [Formula: see text] complete MDP convolutional codes for all code parameters with [Formula: see text] as well as that complete MDP convolutional codes cannot exist if [Formula: see text]. The second main contribution is the presentation of two concrete construction techniques to obtain complete MDP convolutional codes. These constructions work for all code parameters with [Formula: see text] but require that the size of the underlying base field is (sufficiently) large.